Finite Group Databasebeta

← #11878354

Subgroups — #11878354

Order 1152.

856 conjugacy classes of subgroups.

The subgroup lattice has 825 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5833C211yesmaximal, characteristic
2#10594884C211yesmaximal, characteristic, complemented
3#10592938C211yesmaximal, characteristic, complemented
4C3×#5239C211yesmaximal, characteristic, complemented
5#10591653C211yesmaximal, characteristic, complemented
6#10591635C211yesmaximal, characteristic, complemented
7#10591598C211yesmaximal, characteristic, complemented
8#10591558C211yesmaximal, characteristic, complemented
9#10591517C211yesmaximal, characteristic, complemented
10#10591502C211yesmaximal, characteristic, complemented
11#10591460C211yesmaximal, characteristic, complemented
12#10591423C211yesmaximal, characteristic, complemented
13#10591145C211yesmaximal, characteristic, complemented
14#10591135C211yesmaximal, characteristic, complemented
15#10591101C211yesmaximal, characteristic, complemented
16#83428—31nomaximal
17#80238—31nomaximal
18C2×C32×#41C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C2×D3×Dic6C2211yescharacteristic
21C2×#3756C2211yescharacteristic
22C2×#3754C2211yescharacteristic
23#64133C2211yescharacteristic
24C3×#946C2211yescharacteristic
25C3×#946C2211yescharacteristic
26C2×C3×#216C2211yescharacteristic
27C3×#939—21no—
28C3×#939—21no—
29C3×#938C2211yescharacteristic
30C3×#938C2211yescharacteristic
31C2×C3×#214C2211yescharacteristic
32C3×#930—21no—
33C2×C3×C4⋊Dic3C2211yescharacteristic
34C3×#924—21no—
35C3×#924C2211yescharacteristic
36#63969—21no—
37#63959—21no—
38#63884—21no—
39#63857C2211yescharacteristic
40#63856C2211yescharacteristic
41#63841C2211yescharacteristic
42#63839—21no—
43C2×#3711C2211yescharacteristic
44C2×D3×C3⋊C8C2211yescharacteristic
45#63662C2211yescharacteristic
46#63659C2211yescharacteristic
47#63657C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#830C2211yescharacteristic
51#63575C2211yescharacteristic
52#63575C2211yescharacteristic
53#63574C2211yescharacteristic
54#63574C2211yescharacteristic
55#63567C2211yescharacteristic
56#63567C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C3×#537—31no—
62#5833D311yescharacteristic
63#5825—31no—
64#5628—31no—
65C3×#452—31no—
66#5239—31no—
67#5239—31no—
68#5239—61no—
69#5239D311yescharacteristic, complemented
70#5234—31no—
71#5188—31no—
72#5186—31no—
73#5174—31no—
74#5170—31no—
75#5052—31no—
76#5051—31no—
77#5050—31no—
78#5045—31no—
79#5043—31no—
80#5042—31no—
81#5041—31no—
82#5040—31no—
83#5035—31no—
84#4971—31no—
85#4970—31no—
86#4816—31no—
87#4814—31no—
88#4784—31no—
89#4778—31no—
90#4727—31no—
91#4722—31no—
92C32×#41—41no—
93C32×#41—41no—
94C2×C32×Q8C2311yescharacteristic
95C2×C32×D4—21no—
96C2×C32×D4C2311yescharacteristic
97C22×C32×C4—21no—
98C22×C32×C4C2311yescharacteristic
99C2×#634C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C2×C3×#67D411yescharacteristic
103C2×C3×#67D411yescharacteristic
104C22×C3×Dic3—21no—
105C3×#235—41no—
106C3×#235—41no—
107C2×C3×D12D411yescharacteristic
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×Dic6D411yescharacteristic
111C2×C3×Dic6C2311yescharacteristic
112C2×#627—21no—
113C2×D3×Dic3—21no—
114D3×Dic6—41no—
115D3×Dic6—41no—
116#3757—21no—
117#3756—41no—
118#3754—41no—
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120#3750—21no—
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C3×#217—21no—
124C3×#217—21no—
125C3×#217—21no—
126C3×#216—41no—
127C3×#214—41no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×C4⋊Dic3—21no—
131C3×C4⋊Dic3C2311yescharacteristic
132C3×C4⋊Dic3C2311yescharacteristic
133C3×C4⋊Dic3C2311yescharacteristic
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4—21no—
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139#3724—21no—
140Dic3⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143(C2×D3)⋊Dic3—21no—
144Dic32—21no—
145#3711—41no—
146D3×C3⋊C8—41no—
147#3201—91noSylow
148C2×C3×#41—21no—
149C2×C3×#41—31no—
150C2×C3×#41C2×D311yescharacteristic
151C2×C3×#41C2×D311yescharacteristic
152C2×D3×Q8—31no—
153C2×#235C2×D311yescharacteristic
154C22×Dic6—31no—
155C2×C3×Q16—31no—
156C2×C3×SD16—31no—
157C3×C22⋊Q8—31no—
158C3×C22⋊Q8—31no—
159C3×C22⋊Q8—31no—
160C3×C22⋊Q8—61no—
161C3×#121—31no—
162C3×#121—31no—
163C3×#121—61no—
164C3×#121—61no—
165C3×#121—61no—
166C2×C3×C4⋊C4—31no—
167#946—31no—
168#946C2×D311yescharacteristic
169#946C2×D311yescharacteristic
170#944—61no—
171C2×#216—31no—
172C2×#216—31no—
173C2×#216—61no—
174C2×#216C2×D311yescharacteristic
175#939—21no—
176#939—21no—
177#938C2×D311yescharacteristic
178#938C2×D311yescharacteristic
179#936—61no—
180#935—61no—
181#935—61no—
182C2×#214—31no—
183C2×#214—31no—
184C2×#214—61no—
185C2×#214C2×D311yescharacteristic
186#930—21no—
187#926—31no—
188C2×C4⋊Dic3C2×D311yescharacteristic
189#924—21no—
190#924—31no—
191#924—31no—
192#924—31no—
193#924—31no—
194#924—61no—
195#924C2×D311yescharacteristic
196C2×#208—31no—
197C22×C3⋊C8—31no—
198C2×ΓL(1,𝔽25)—31no—
199C2×D3×C8—31no—
200#897—31no—
201#894—61no—
202#892—31no—
203#888—61no—
204#885—61no—
205#883—61no—
206C3×#103—31no—
207C3×#102—31no—
208C3×C22⋊C8—31no—
209#835—31no—
210#835—31no—
211#835—31no—
212#835—31no—
213#835—61no—
214#835C2×D311yescharacteristic
215#832—31no—
216#832—31no—
217#832—61no—
218#832C2×D311yescharacteristic
219#830—31no—
220#830—31no—
221#830—31no—
222#830—31no—
223#830—61no—
224#830C2×D311yescharacteristic
225(C2×D3)⋊C8—31no—
226(C2×D3)⋊C8—31no—
227#818—31no—
228#818—31no—
229#816—31no—
230#816—31no—
231#810—31no—
232#810—31no—
233#810—31no—
234#810—31no—
235#808—31no—
236#808—31no—
237#808—31no—
238#808—31no—
239#807—31no—
240#807—31no—
241C23×C32—21no—
242C23×C32C2×D411yescharacteristic
243C22×C3×D3C2×D411yescharacteristic
244C22×C3×D3C2×D411yescharacteristic
245C32×Q8—21no—
246C32×Q8—21no—
247C32×D4—21no—
248C32×D4—21no—
249C32×D4—42no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—42no—
254C2×C32×C4C2×D411yescharacteristic
255C2×C32×C4C2411yescharacteristic
256C2×C3⋊Dic3—21no—
257C2×C3⋊Dic3—21no—
258#634—21no—
259#634—21no—
260C3×#67—41no—
261C3×#67—41no—
262C3×#67—81no—
263C3×#67—81no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—81no—
269C2×C3×Dic3C2×D411yescharacteristic
270C2×C3×Dic3C2×D411yescharacteristic
271C3×D12—41no—
272C3×C4×D3—21no—
273C3×C4×D3—21no—
274C3×C4×D3—21no—
275C3×C4×D3—21no—
276C3×Dic6—21no—
277C3×Dic6—21no—
278C3×Dic6—41no—
279#627—42no—
280D3×Dic3—42no—
281C3⋊(C3⋊C8)—21no—
282C3⋊(C3⋊C8)—21no—
283C3×C3⋊C8—21no—
284C3×C3⋊C8—21no—
285#537—31no—
286#536—91no—
287#485—91no—
288#484—91no—
289#483—91no—
290#482—91no—
291#470—91no—
292#468—91no—
293#467—91no—
294#465—91no—
295#452—31no—
296#452—91no—
297#451—91no—
298#448—91no—
299#408—91no—
300C3×#41—41no—
301C3×#41—41no—
302C3×#41—41no—
303C3×#41—41no—
304C3×#41—42no—
305C3×#41—42no—
306C3×#41—121no—
307C3×#41—121no—
308C2×C3×Q8—21no—
309C2×C3×Q8—31no—
310C2×C3×Q8—31no—
311C2×C3×Q8C22×D311yescharacteristic
312C2×C3×Q8C22×D311yescharacteristic
313C2×C3×D4—21no—
314C2×C3×D4—21no—
315C2×C3×D4—21no—
316C2×C3×D4—31no—
317C2×C3×D4—31no—
318C2×C3×D4—31no—
319C2×C3×D4—41no—
320C2×C3×D4—61no—
321C2×C3×D4—61no—
322C2×C3×D4C22×D311yescharacteristic
323C2×C3×D4C22×D311yescharacteristic
324C22×C3×C4—21no—
325C22×C3×C4—21no—
326C22×C3×C4—21no—
327C22×C3×C4—31no—
328C22×C3×C4—31no—
329C22×C3×C4—41no—
330C22×C3×C4—61no—
331C22×C3×C4C22×D311yescharacteristic
332C22×C3×C4C22×D311yescharacteristic
333C2×#67—21no—
334C2×#67—21no—
335C2×#67#6711yescharacteristic
336C2×#67#6711yescharacteristic
337C22×Dic3—21no—
338C22×Dic3—61no—
339D3×Q8—121no—
340D3×Q8—121no—
341#235—41no—
342#235—41no—
343C2×D12#6711yescharacteristic
344C2×C4×D3—61no—
345C2×C4×D3C22×D311yescharacteristic
346C2×C4×D3C22×D311yescharacteristic
347C2×Dic6—31no—
348C2×Dic6—31no—
349C2×Dic6—61no—
350C2×Dic6—61no—
351C2×Dic6—61no—
352C2×Dic6—121no—
353C2×Dic6—121no—
354C2×Dic6#6711yescharacteristic
355C2×Dic6C22×D311yescharacteristic
356C3×Q16—121no—
357C3×SD16—121no—
358C2×C3×C8—31no—
359C2×C3×C8—31no—
360C3×C4⋊C4—31no—
361C3×C4⋊C4—31no—
362C3×C4⋊C4—31no—
363C3×C4⋊C4—61no—
364C3×C4⋊C4—61no—
365C3×C4⋊C4—61no—
366C3×C4⋊C4—61no—
367C3×C22⋊C4—61no—
368C3×C22⋊C4—61no—
369C3×C22⋊C4—61no—
370C3×C22⋊C4—61no—
371C3×C22⋊C4—61no—
372#217—21no—
373#217—21no—
374#217—21no—
375#217—61no—
376#217—61no—
377#217—61no—
378#217—61no—
379#217—61no—
380#217—121no—
381#216—41no—
382#216—121no—
383#216—121no—
384#216—122no—
385#214—41no—
386#214—121no—
387#214—121no—
388#214—122no—
389(C2×D3)⋊C4—21no—
390(C2×D3)⋊C4—21no—
391(C2×D3)⋊C4—61no—
392(C2×D3)⋊C4—61no—
393(C2×D3)⋊C4—61no—
394C4⋊Dic3—21no—
395C4⋊Dic3—31no—
396C4⋊Dic3—31no—
397C4⋊Dic3—61no—
398C4⋊Dic3—61no—
399C4⋊Dic3C22×D311yescharacteristic
400C4⋊Dic3C22×D311yescharacteristic
401C4⋊Dic3C22×D311yescharacteristic
402Dic3⋊C4—21no—
403Dic3⋊C4—21no—
404Dic3⋊C4—21no—
405Dic3⋊C4—61no—
406Dic3⋊C4—61no—
407Dic3⋊C4—61no—
408Dic3⋊C4—61no—
409Dic3⋊C4—61no—
410Dic3⋊C4—121no—
411C4×Dic3—61no—
412C4×Dic3—61no—
413#208—121no—
414C2×C3⋊C8—31no—
415C2×C3⋊C8—31no—
416C2×C3⋊C8—31no—
417C2×C3⋊C8—31no—
418C2×C3⋊C8—61no—
419C2×C3⋊C8—61no—
420C2×C3⋊C8—121no—
421C2×C3⋊C8C22×D311yescharacteristic
422C2×C3⋊C8C22×D311yescharacteristic
423ΓL(1,𝔽25)—121no—
424D3×C8—121no—
425C22×C32—21no—
426C22×C32—21no—
427C22×C32—21no—
428C22×C32—41no—
429C22×C32—41no—
430C22×C32—41no—
431C22×C32C22×D411yescharacteristic
432C2×C3×D3—21no—
433C2×C3×D3—21no—
434C2×C3×D3—21no—
435C2×C3×D3—21no—
436C2×C3×D3—21no—
437C2×C3×D3—21no—
438C32×C4—21no—
439C32×C4—41no—
440C32×C4H(5,𝔽2)11yescharacteristic
441C32×C4H(5,𝔽2)11yescharacteristic
442C3⋊Dic3—41no—
443C3⋊Dic3—41no—
444C3×Dic3—21no—
445C3×Dic3—21no—
446C3×Dic3—41no—
447C3×Dic3—41no—
448C3×Dic3—41no—
449C3×Dic3—41no—
450C2×#41—31no—
451C2×#41D3211yescharacteristic
452C22×Q8—91no—
453C2×Q16—31no—
454C2×Q16—91no—
455C2×SD16—31no—
456C2×SD16—91no—
457C2×M16—91no—
458C22×C8—91no—
459C4⋊Q8—181no—
460#124—181no—
461#123—181no—
462#123—181no—
463C22⋊Q8—31no—
464C22⋊Q8—31no—
465C22⋊Q8—31no—
466C22⋊Q8—61no—
467C22⋊Q8—91no—
468C22⋊Q8—91no—
469C22⋊Q8—91no—
470#121—31no—
471#121—31no—
472#121—61no—
473#121—61no—
474#121—61no—
475#117—91no—
476C2×C4⋊C4—31no—
477#107—91no—
478#107—91no—
479#106—91no—
480#106—91no—
481#103—31no—
482#103—91no—
483#103—91no—
484#103—91no—
485#103—91no—
486#103—91no—
487#102—31no—
488#102—91no—
489C22⋊C8—31no—
490C22⋊C8—91no—
491C22⋊C8—91no—
492C22⋊C8—91no—
493C23×C3—21no—
494C23×C3—21no—
495C23×C3—21no—
496C23×C3—31no—
497C23×C3—31no—
498C23×C3—41no—
499C23×C3D3×D411yescharacteristic
500C23×C3C2×#6711yescharacteristic
501C22×D3C2×#6711yescharacteristic
502C22×D3C2×#6711yescharacteristic
503C3×Q8—22no—
504C3×Q8—21no—
505C3×Q8—21no—
506C3×Q8—21no—
507C3×Q8—21no—
508C3×Q8—41no—
509C3×Q8—61no—
510C3×Q8—61no—
511C3×Q8—121no—
512C3×D4—22no—
513C3×D4—21no—
514C3×D4—21no—
515C3×D4—21no—
516C3×D4—21no—
517C3×D4—41no—
518C3×D4—42no—
519C3×D4—42no—
520C3×D4—44no—
521C3×D4—121no—
522C3×D4—121no—
523C3×D4—121no—
524C3×D4—241no—
525C3×D4—241no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—31no—
535C2×C3×C4—31no—
536C2×C3×C4—41no—
537C2×C3×C4—41no—
538C2×C3×C4—41no—
539C2×C3×C4—42no—
540C2×C3×C4—42no—
541C2×C3×C4—44no—
542C2×C3×C4—61no—
543C2×C3×C4—61no—
544C2×C3×C4—61no—
545C2×C3×C4—61no—
546C2×C3×C4—61no—
547C2×C3×C4—61no—
548C2×C3×C4—61no—
549C2×C3×C4—61no—
550C2×C3×C4—241no—
551C2×C3×C4D3×D411yescharacteristic
552C2×C3×C4C2×#6711yescharacteristic
553C2×C3×C4C23×D311yescharacteristic
554C2×C3×C4C23×D311yescharacteristic
555#67—41no—
556#67—41no—
557#67—81no—
558#67—81no—
559C2×Dic3—21no—
560C2×Dic3—21no—
561C2×Dic3—21no—
562C2×Dic3—21no—
563C2×Dic3—61no—
564C2×Dic3—61no—
565C2×Dic3—61no—
566C2×Dic3—61no—
567C2×Dic3—81no—
568C2×Dic3—121no—
569C2×Dic3—121no—
570C2×Dic3—122no—
571C2×Dic3C2×#6711yescharacteristic
572C2×Dic3C2×#6711yescharacteristic
573D12—41no—
574C4×D3—21no—
575C4×D3—21no—
576C4×D3—21no—
577C4×D3—21no—
578C4×D3—122no—
579Dic6—21no—
580Dic6—21no—
581Dic6—41no—
582Dic6—61no—
583Dic6—61no—
584Dic6—61no—
585Dic6—61no—
586Dic6—121no—
587Dic6—121no—
588Dic6—122no—
589Dic6—122no—
590C3×C8—61no—
591C3×C8—61no—
592C3⋊C8—21no—
593C3⋊C8—21no—
594C3⋊C8—61no—
595C3⋊C8—61no—
596C3⋊C8—61no—
597C3⋊C8—61no—
598C3⋊C8—121no—
599C3⋊C8—121no—
600C2×C32—41no—
601C2×C32—81no—
602C2×C32#53411yescharacteristic
603C2×C32#57711yescharacteristic
604C2×C32#57811yescharacteristic
605C3×D3—41no—
606C3×D3—41no—
607#41—41no—
608#41—41no—
609#41—121no—
610#41—121no—
611C2×Q8—31no—
612C2×Q8—31no—
613C2×Q8—91no—
614C2×Q8—181no—
615C2×Q8—361no—
616C2×Q8—361no—
617C2×Q8C2×D3211yescharacteristic
618C2×D4—21no—
619C2×D4—31no—
620C2×D4—31no—
621C2×D4—31no—
622C2×D4—61no—
623C2×D4—61no—
624C2×D4C2×D3211yescharacteristic
625C22×C4—21no—
626C22×C4—31no—
627C22×C4—31no—
628C22×C4—61no—
629C22×C4—181no—
630C22×C4C2×D3211yescharacteristic
631Q16—121no—
632Q16—361no—
633SD16—121no—
634SD16—361no—
635M16—361no—
636C2×C8—31no—
637C2×C8—31no—
638C2×C8—91no—
639C2×C8—91no—
640C2×C8—361no—
641C4⋊C4—31no—
642C4⋊C4—31no—
643C4⋊C4—31no—
644C4⋊C4—61no—
645C4⋊C4—61no—
646C4⋊C4—61no—
647C4⋊C4—61no—
648C4⋊C4—91no—
649C4⋊C4—181no—
650C4⋊C4—181no—
651C4⋊C4—181no—
652C22⋊C4—61no—
653C22⋊C4—61no—
654C22⋊C4—61no—
655C22⋊C4—61no—
656C22⋊C4—61no—
657C22⋊C4—181no—
658C22⋊C4—181no—
659C22⋊C4—181no—
660C22⋊C4—181no—
661C42—181no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—21no—
665C22×C3—21no—
666C22×C3—21no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—41no—
670C22×C3—41no—
671C22×C3—41no—
672C22×C3—42no—
673C22×C3—41no—
674C22×C3—41no—
675C22×C3—41no—
676C22×C3—41no—
677C22×C3—41no—
678C22×C3—41no—
679C22×C3—61no—
680C22×C3—61no—
681C22×C3—61no—
682C22×C3—61no—
683C22×C3—61no—
684C22×C3—61no—
685C22×C3—81no—
686C22×C3—81no—
687C22×C3C2×D3×D411yescharacteristic
688C22×C3C22×#6711yescharacteristic
689C2×D3—21no—
690C2×D3—21no—
691C2×D3—21no—
692C2×D3—21no—
693C2×D3—21no—
694C2×D3—21no—
695C3×C4—21no—
696C3×C4—21no—
697C3×C4—21no—
698C3×C4—21no—
699C3×C4—41no—
700C3×C4—42no—
701C3×C4—41no—
702C3×C4—41no—
703C3×C4—61no—
704C3×C4—61no—
705C3×C4—121no—
706C3×C4—121no—
707C3×C4—121no—
708C3×C4—121no—
709C3×C4#100411yescharacteristic
710C3×C4#100411yescharacteristic
711C3×C4#100411yescharacteristic
712C3×C4#100411yescharacteristic
713Dic3—21no—
714Dic3—21no—
715Dic3—41no—
716Dic3—41no—
717Dic3—41no—
718Dic3—41no—
719Dic3—121no—
720Dic3—121no—
721Dic3—121no—
722Dic3—121no—
723Dic3—241no—
724Dic3—241no—
725C32#320111yescharacteristic, complemented, Sylow
726C23—21no—
727C23—31no—
728C23—31no—
729C23D3×#6711yescharacteristic
730Q8—21no—
731Q8—21no—
732Q8—61no—
733Q8—61no—
734Q8—121no—
735Q8—181no—
736Q8—181no—
737Q8—362no—
738D4—21no—
739D4—21no—
740D4—42no—
741D4—121no—
742D4—121no—
743D4—121no—
744D4—241no—
745D4—241no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—31no—
750C2×C4—31no—
751C2×C4—42no—
752C2×C4—61no—
753C2×C4—61no—
754C2×C4—61no—
755C2×C4—61no—
756C2×C4—61no—
757C2×C4—61no—
758C2×C4—61no—
759C2×C4—61no—
760C2×C4—181no—
761C2×C4—181no—
762C2×C4—241no—
763C2×C4—362no—
764C2×C4D3×#6711yescharacteristic
765C2×C4C22×D3211yescharacteristic
766C8—61no—
767C8—61no—
768C8—181no—
769C8—181no—
770C2×C3—21no—
771C2×C3—21no—
772C2×C3—21no—
773C2×C3—41no—
774C2×C3—41no—
775C2×C3—81no—
776C2×C3—82no—
777C2×C3—81no—
778C2×C3—81no—
779C2×C3—121no—
780C2×C3—121no—
781C2×C3#558911yescharacteristic
782C2×C3#577111yescharacteristic
783C2×C3#577811yescharacteristic
784C2×C3#580411yescharacteristic
785C2×C3#583611yescharacteristic
786C2×C3#583811yescharacteristic
787D3—41no—
788D3—41no—
789C22—21no—
790C22—21no—
791C22—21no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—61no—
796C22—61no—
797C22—61no—
798C22—61no—
799C22—61no—
800C22—61no—
801C22C2×D3×#6711yescharacteristic
802C4—21no—
803C4—41no—
804C4—61no—
805C4—61no—
806C4—121no—
807C4—121no—
808C4—121no—
809C4—121no—
810C4—361no—
811C4—361no—
812C4#6433011yescharacteristic
813C4#6433011yescharacteristic
814C3—21no—
815C3#8023811yescharacteristic, complemented
816C3#8342811yescharacteristic, complemented
817C2—41no—
818C2—81no—
819C2—121no—
820C2—121no—
821C2#1059546411yescharacteristic
822C2#1059546711yescharacteristic
823C2#1059552411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
prime radicalC3×#5833C2
hypercenterC2×#41D32
hypocenterC32#3201
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #10594884C2semidirect
3. #10592938C2semidirect
4. C3×#5239C2semidirect
5. #10591653C2semidirect
6. #10591635C2semidirect
7. #10591598C2semidirect
8. #10591558C2semidirect
9. #10591517C2semidirect
10. #10591502C2semidirect
11. #10591460C2semidirect
12. #10591423C2semidirect
13. #10591145C2semidirect
14. #10591135C2semidirect
15. #10591101C2semidirect
69. #5239D3semidirect
725. C32#3201semidirect
815. C3#80238semidirect
816. C3#83428semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3×#58332
#105948842
#105929382
C3×#52392
#105916532
#105916352
#105915982
#105915582
#105915172
#105915022
#105914602
#105914232
#105911452
#105911352
#105911012
#834283
#802383